Study Guide
Learning Objectives
- Estimate period/frequency from consecutive maxima or minima (3.7.A.1).
- Estimate amplitude and vertical shift from max/min (3.7.A.2).
- Estimate phase shift using an input-output pair (3.7.A.3).
- Build models with technology or key-value estimation (3.7.A.4).
- Predict within a contextual domain and justify (3.7.A.5).
Suggested Practice Sequence
1. Read max/min from a graph or table; find midline and amplitude. 2. Measure period from consecutive peaks or troughs. 3. Fit $y=a\sin(b(\theta+c))+d$ or cosine form using 3.6 language. 4. Use one known point to solve for phase $c$. 5. Predict at a new input; state domain limits. 6. Compare manual estimate vs technology regression.
Classroom / Check-In Moves
- "Max/min $\rightarrow$ midline/amp" then "peak-to-peak $\rightarrow$ period."
- One-point phase fit exit ticket.
- Domain/prediction reasonableness check.
Misconception Watch-List
- Confusing amplitude with maximum when midline is not zero.
- Using peak-to-trough distance as period.
- Ignoring contextual domain on predictions.
- Forgetting to justify model choice with periodic evidence.
Vocabulary to Own
- contextual domain
- consecutive maxima/minima
- amplitude; vertical shift; period; phase shift
- sinusoidal regression
- prediction; dependent/independent variable
Materials Map
- Practice: construct and predict
- Word: real periodic contexts
- Mixed / multi-*: link to 3.5-3.6 parameters
- Review & practice test: model-building fluency
- Interactive: parameter and prediction checks